Involutory and invertible fuzzy BCK-algebras
type: Item
instance of: scholarly article
title: Involutory and invertible fuzzy BCK-algebras
zbMATH Open document ID: 0968.06015
DOI: 10.1016/S0165-0114(98)00406-0
author: Xiaolong Xin
author: Young Bae Jun
published in: Fuzzy Sets and Systems
publication date: 2001-09-13T00:00:00Z
review text: A fuzzy ideal \(\mu\) of a commutative BCK-algebra \(X\) is said to be involutory if \(\mu^{++}=\mu\), where \(\mu^+ (x)=1-\inf\{\mu(y) |y\wedge x=0\}\). In bounded implicative BCK-algebras all fuzzy ideals are involutory. Moreover, if in a commutative BCK-algebra \(X\) all fuzzy ideals are involutory and \(\mu^+\) is a fuzzy ideal for every fuzzy ideal \(\mu\), then the set of all fuzzy ideals of \(X\) is a distributive lattice with respect to the fuzzy operations \(\cup\) and \(\cap\).
Mathematics Subject Classification ID: 06F35
zbMATH DE Number: 1563552
zbMATH Keywords: BCK-algebra
zbMATH Keywords: fuzzy ideal
reviewed by: Wiesław A. Dudek
MaRDI profile type: Publication
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full work available at URL: s0165-0114(98)00406-0
OpenAlex ID: W2014569286
description: scientific article; zbMATH DE number 1563552